Infinite impulse response (IIR) digital filters, and in particular, biquad infinite impulse response (BIIR) filters, have been widely used in the field of communications, among other applications. For example, such digital filters are often used to remove noise, enhance communication signals, and/or synthesize communication signals. Compared to a finite impulse response (FIR) filter, an IIR filter is generally much more efficient in terms of achieving certain performance characteristics with a given filter order. This is primarily because an IIR filter incorporates feedback and is capable of realizing both poles and zeros of a system transfer function, whereas an FIR filter can only realize zeros of a transfer function. Moreover, IIR filters use a smaller number of coefficients to obtain a required impulse response of a desired filter.
Higher order IIR filters can be obtained by cascading multiple biquad IIR filters with appropriate coefficients. Another way to design higher-order IIR filters is to employ a single complex section. This latter approach is often referred to as a direct form implementation. The cascaded biquad implementation generally executes slower than the direct form implementation but generates smaller numerical errors than the direct form implementation. Another disadvantage of the direct form implementation is that the poles of such single-stage high-order polynomials get increasingly sensitive to quantization errors; second-order polynomial sections (i.e., biquads) are less sensitive to quantization effects.
One significant disadvantage of a BIIR implementation in a vector processor environment is a requirement for sequential processing of output samples. Conventional direct form implementation BIIR filter implementations utilize only a relatively small subset (e.g., three) of the total number of multipliers available. This implementation is inefficient, and is prone to execution stalls, and hence is undesirable.